We construct updated solar models with different sets of solar abundances, including the most recent determinations by Asplund et al. The latter work predicts a larger (~10%) solar metallicity compared to previous measurements by the same authors but significantly lower (~25%) than the recommended value from a decade ago by Grevesse & Sauval. We compare the results of our models with determinations of the solar structure inferred through helioseismology measurements. The model that uses the most recent solar abundance determinations predicts the base of the solar convective envelope to be located at R _CZ = 0.724 R _☉ and a surface helium mass fraction of Y _surf = 0.231. These results are in conflict with helioseismology data (R _CZ = 0.713 ± 0.001 R _☉ and Y _surf = 0.2485 ± 0.0035) at 5σ and 11σ levels, respectively. Using the new solar abundances, we calculate the magnitude by which radiative opacities should be modified in order to restore agreement with helioseismology. We find that a maximum change of ~15% at the base of the convective zone is required with a smooth decrease toward the core, where the change needed is ~5%. The required change at the base of the convective envelope is about half the value estimated previously. We also present the solar neutrino fluxes predicted by the new models. The most important changes brought about by the new solar abundances are the increase by ~10% in the predicted ¹³N and ¹⁵O fluxes that arise mostly due to the increase in the C and N abundances in the newly determined solar composition.